Second Order Linear Recurring Sequences in Hypercomplex Numbers

1998 ◽  
pp. 337-351
Author(s):  
Klaus Scheicher
Keyword(s):  
Second Order ◽  
Hypercomplex Numbers ◽  
Order Linear ◽  
Linear Recurring Sequences

Linear Recurring Sequences and Explicit Factors of x2nd−1 in 𝔽q[x]

2020 ◽  
Vol 27 (03) ◽  
pp. 563-574
Author(s):  
Manjit Singh
Keyword(s):  
Field Theory ◽  
Positive Integer ◽  
Finite Field ◽  
Finite Fields ◽  
Second Order ◽  
Order Linear ◽  
Linear Recurring Sequences

Let 𝔽q be a finite field of odd characteristic containing q elements, and n be a positive integer. An important problem in finite field theory is to factorize xn − 1 into the product of irreducible factors over a finite field. Beyond the realm of theoretical needs, the availability of coefficients of irreducible factors over finite fields is also very important for applications. In this paper, we introduce second order linear recurring sequences in 𝔽q and reformulate the explicit factorization of [Formula: see text] over 𝔽q in such a way that the coefficients of its irreducible factors can be determined from these sequences when d is an odd divisor of q + 1.

Bases for Second Order Linear ODEs

2020 ◽  
Vol 127 (9) ◽  
pp. 849-849
Author(s):  
Peter McGrath
Keyword(s):  
Second Order ◽  
Order Linear ◽  
Linear Odes
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